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multivariate normal distribution


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Random variables X1, X2,…, Xn (each with ranges from−∞ to ∞) have a multivariate normal distribution if their joint probability density function f is given by where x is the n×1 vector of values, μ is the n×1 vector of means, Σ is the n×n variance–covariance matrix, and det(Σ) is the determinant of Σ.

For the special case of the bivariate normal distribution, with random variables X and Y, the joint probability density function f is given by where the mean and variance of X are μx and σ2x, the mean and variance of Y are μy and σy2, and ρ is the correlation coefficient between the two variables.

Subjects: Probability and Statistics.


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